• Created by Unknown User (adamsa@mit.edu), last modified by Unknown User (astrocrg@mit.edu) on Feb 13, 2019 19:06

On 2/10/2019, some initial, rough estimates were calculated by Andrew A. and Shannon C. The analysis intends to minimize changes to the Hermes architecture and get initial estimates for masses of 2nd stage parts. 

*** Todo: make equations much nicer

Assumptions: 

Hermes II architecture for both stages

2 km/s delta-V requirement to get to 100km (ideal is 1.4 km/s, +200m/s gravity losses (20s total burn time), +200 m/s drag losses, +200 m/s margin for cosine losses)

Cherry Limeade Isp: 226s --> exhaust velocity near 2200 m/s

O3400 CTI motor – propellant mass estimate for S2 

Summary of calculations: 

SEE APPENDIX BELOW FOR MASS ESTIMATION SPREADSHEETS

To calculate the delta-V for a staged rocket, we need to know the propellant mass fraction for the rocket and the Isp of the propellant. To calculate the dV for the first stage, we need to consider the total mass of both stages:

m0 = m01 + m02 = 163.5 + 63.5 lbs = 227 lbs                          

We estimate the propellant mass of the first stage (mp1) to be 78.75 lbs, and using a rearrangement of the rocket equation, we get the following: 

mf1 = m0 - mp1 + m02 = 148.25 lbs

dV1 = c ln (m0/mf1) = ~950 m/s

This leaves 1050 m/s to be covered by the second stage. Using same equation, but applied to only the second stage, we conclude: 

mf2 = m02 / e^(dV2/c) = 39 lbs 

Using the O3400 as a datum for the propellant mass of the second stage – we get that the dry mass available is almost exactly as calculated. This is coincidental - if we increase the dV2 value, we get smaller dry mass with the same m02. 

However, we should still strive to improve the second stage dry mass, as we'll likely increase the mass of the rocket as time goes on, and there may be more drag or cosine losses due to staging than anticipated! 

Recommendations for S2

The following recommendations are given for the second stage to improve its performance:   

Recovery 6.6 --> 4.4 lb

Payload 4.4 --> 2.2 lb

Propellant: 24.2 --> 27 lb

Structures: 9.4 --> 7.4 lb

Avionics: 3.5 --> 3 lb

Propulsion: 15.4lb (no change)

This led to a vehicle with 59.4 lb wet mass, and 32.4 lb dry mass. (~6.6 lb of margin). This would give us significant delta V margin. (dV2 = c ln(m02/mf2) = ~1300 m/s --> +250 m/s margin)

This could be achieved mostly by shortening the rocket, compacting the AV bay, and lengthening the motor while lightening incidental case hardware (carrier, boattail, bolts, retention ring) 

These are preliminary estimates with plenty of assumptions made, all intended to inform future analysis. 

Semi-known potential changes: 

The following factors may improve the available mass of the second stage:

  • Additional propellant mass on the first stage due to monolithic geometry 
  • Change in Isp for sustainer motor propellant 
  • Better fin analysis and optimization
  • Nose cone layup improvements
  • Data from main parachute deployment to understand loads on rocket --> decrease structural mass

Appendix – Mass Estimation:

Hermes III Mass estimation: 2/10 Hermes II Mass budget with the following anticipated changes:

-8.5 lbs: switch motor case to 3/16" wall 

-2.5 lbs: no Load cell

-4 lbs: no NC

-6.6 lbs: no payload stack

+2 lbs: interstage shell

+2 lbs: deployment mech

+5 lbs: add'l propellant

https://docs.google.com/spreadsheets/d/1re68QEHMAFCbQYufKbnk3cOaRIJo-JWThO-DMbLWqk8/edit#gid=0

Estimate: 163.5 lbs


S2 Mass estimation assumptions:

Propellant mass of O3400 (w/ Isp of Cherry Limeade) (24.2 lb)

Case mass of O3400 + 2.2 lb (15.4 lb) 

3ft of G12 fiberglass tube (12.8oz/ft – Madcow rocketry) (2.4 lb)

NC (2 lb) 

FC (3 lb)

Bulkhead / coupler (1 lb)

Hoist ring and Misc. hardware (1 lb)

Recovery system  (6.6 lb)

Payload (4.4 lb)

AV bay (1.5 lb)

Active Controls (if needed) (2 lb)

Initial estimate: 63.5 lbs

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